Trying to understand the shape of the universe is like trying to conceptualize how infinity works for us – it makes most people’s heads hurt. Space expands, but expands inside of what? The best we can conceptualize our own universe as is a balloon with dots on it, or as a sphere of raisin bread. The best we can think of to describe our universe is as a sphere, since spacetime is curved and follows the geometry of the surface of a sphere. A sphere, like the globe, has no edge, but it is bounded; it has a definite area. The universe has no edge and it is boundless. Our models are insufficient right now, since the scales of distance are so large, and there is less that we can observe and falsify.
We are faced with an incomprehensible Lovecraftian universe again. For example, a dog can comprehend a calculator in his or her own way. She knows she can bite it, that the front is rubbery, and the back is hard, but she can never understand the circuitry within the calculator, how it works or how to do equations on it. Us humans can understand the universe in our own way. How we understand the universe can be totally wrong or woefully incomplete, but our understanding could remain the way it is forever, because that’s just how we understand things. That’s the limit of our knowledge and we will never know better, like the dog chewing the calculator.
Even if an alien race, were to contact us, they could teach us forever and we still wouldn’t fully understand, the same way a dog will never understand how to use a calculator. Our brains are model 10 and theirs are model 100. They might love us, but they could only teach us so much, the same way we love dogs but can only train them to do so much.
Despite our limitations, our species has come so far. Our mathematical models offer us the best way to understand the universe and have revealed so much to us up to this point. We know nature and the universe work on power laws. It is possible there is a limit to human brain power, but if there is, we haven’t reached it yet. In fact, we may be very far away from reaching said limit.
We need to invest selectively in bigger telescopes, more satellites and better physics and astrophysics departments; we need to see farther. We can only see so far in our galaxy and in our universe with the Hubble and our infrared, X-ray and gamma telescopes. We don’t know enough. We need to get to the bottom of these supposed mysteries of the universe, like black holes, tachyons, neutrinos, dark matter, and the expanding universe.